报 告 人：胡洪晓
报告题目：A comparison of deterministic and stochastic models for predator-prey species with disease in the prey
男，博士，讲师，硕士生导师。2011年6月于同济大学数学系获理学博士学位。2011年7月到上海理工大学理学院工作至今。目前主要研究方向为生物数学、随机微分方程。已在Nonlinear Analysis、Journal of Real World Applications、Journal of Mathematical Analysis and Applications、Proceedings of the American Mathematical Society等国际著名期刊上发表SCI论文十余篇，主持一项国家自然科学基金 (青年基金)。
Abstract: A predator-prey model, where prey species is subjected to an SI parasitic infection with the infected prey being more vulnerable to be predated, is developed, analyzed and simulated. First, a deterministic model is formulated, then analogous stochastic models. The deterministic model is a system of ordinary differential equations for predator-prey species with disease in the prey. Thresholds are identified which determine when an infected prey successfully invades into a persistent disease-free predator-prey system or a predator species successfully invades into a prey system with SI form disease infection. New stochastic models are derived in the form of continuous-time Markov chains and stochastic differential equations. Branching process theory is applied to the continuous-time Markov chain models to estimate probabilities for disease outbreak or predator species invasion. Finally, some numerical simulations are introduced to illustrate the main results and to highlight some of the differences between the stochastic and deterministic models.